Question

A particle moves with constant speed 20 m/s
for 5 sec then after it covers a distance 200
m with constant speed 10 m/s. Calculate its
average speed.​

Answer 1

Topic :-

Kinematics in one Dimension

Given :-

A particle moves with constant speed 20 m/s for 5 seconds then it covers a distance of 200 metres with constant speed 10 m/s.

To Find :-

Average Speed of the particle.

Formula to be Used :-

$\boxed{\sf{Average\:\:Speed=\dfrac{Total \:\: Distance}{Total\:\:Time}}}$

$\sf{Distance=Speed \times Time}$

$\sf{Time=\dfrac{Distance}{Speed}}$

Solution :-

Distance covered in first 5 seconds with speed of 20 m/s,

• Speed = 20 m/s

• Time = 5 seconds

Distance = Speed × Time

Distance = 20 × 5

Distance = 100 metres

Time taken to travel 200 metres with 10 m/s speed,

• Distance = 200 metres

• Speed = 10 m/s

$\sf{Time=\dfrac{Distance}{Speed}}$

$\sf{Time=\dfrac{200}{10}}$

$\sf{Time=20\:\:seconds}$

So, total distance travelled = ( 100 + 200 ) metres.

Total Distance travelled = 300 metres

Total Time taken = ( 5 + 20 ) seconds.

Total Time Taken = 25 seconds

Now,

Applying the formula,

$\boxed{\sf{Average\:\:Speed=\dfrac{Total \:\: Distance}{Total\:\:Time}}}$

$\sf{Average\:\:Speed=\dfrac{300\:\:metres}{25\:\:seconds}}$

$\sf{Average\:\:Speed=12\:\:m/s}$

Answer :-

So, the average speed of particle is 12 m/s.